Linking Adjectives and Participles

This question has less to do with what sounds natural (I'm sure there are better ways to make this statement) and more to do with syntax. I'm wondering what would be the proper conjugation to string together adjectives and adjectival verbs. For instance:

彼は誰かの好きな死んだ人だった。

I apologize for this most certainly being a dreadfully poorly written sentence (suggestions for better wording are welcome), but I'm more interested in the appropriate way to use participles to make descriptor chains.

I still cannot come up with the situation described in that sentence (especially "someone"), but if I may ignore that,
故人は、誰かに愛された人でした。 The deceased was a person who was loved by someone.
or
彼は、生前（せいぜん）誰かに愛された人でした。 He was loved by someone when he was alive.

But if you must use 好きな, switch 誰かに愛された人 with 誰かの好きな人, but it sounds really awkward. It really needs decent context.

It would be more decent if the sentence was like
故人は、多くの国民に愛された有名な音楽家でした。 The deceased was a famous musician who was loved by many nations.

これは有名な読めるの犬です。- This is a/the famous dog that can read. (This is a/the famous and able-to-read dog.)

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You cannot connect a verb with a noun by の here. And 読める犬 sounds a bit awkward but I do not know why.
これは有名な「読む」犬です。

Two things you may want to keep in mind.
1) Usually in Japanese we add an object there for 読む, such as 「本を読む」犬, 「新聞を読む」犬, or maybe 「字が読める」犬.
2) I'd say この犬は instead of これは unless you are showing a picture or a video to mean "this picture" for これ.

Awkwardness aside, what would be the proper way to connect an adjective to an attributive verb, such as in that sentence?

Would it be 有名な? or 有名で? or something completely different?

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Ah, I think I finally understood what you were asking about. If you mean you want to connect more than one adjectives, you can use で/て.
彼女はまじめで礼儀正しいです。 （まじめな+礼儀正しい） （→彼女はまじめで礼儀正しい人です。）
私の先生は優しくてきれいです。（優しい+きれいな） （→私の先生は優しくてきれいな人です。）
But 「有名な」 and 「読む」 are different （the former is a na-adjective, the latter is a verb modifying the following noun, or as you said, an attributive verb) and you do not list them like you do with two adjectives. So, 「有名な」 should stay as 「有名な」 and do not change to 「有名で」.

これは有名な読めるの犬です。- This is a/the famous dog that can read. (This is a/the famous and able-to-read dog.)

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See yours is This is adj. + noun + that relative clause.
You can set the relative clause （文字が）読める directly prior to 犬. And add an adjective 有名な: これは有名な（文字が）読める犬です。
e.g. The guy who controlled the village was dead. 村を支配した男は死んだ。

Your first question 'He, loved by someone, was dead' is very difficult, almost special-A. See this is different from the cases above.

Welcome to my correction.
In the dog's sample, what is famous? The dog. So let's join it closer to the dog: これは文字が読める有名な犬です。This is more accurate.
In これは有名な文字が読める犬です。, this one arises a possibility that the famous is the words. Most of us figure out the dog must be famous because it can read..but in other sentences you need to be more accurate, confusion may arise. Whatever, doing so is better. Sorry I noticed after I had posted.